{"product_id":"introduction-to-finite-element-analysis-isbn-9780470977286","title":"Introduction to Finite Element Analysis","description":"\u003cb\u003eWhen using numerical simulation to make a decision, how can its reliability be determined? What are the common pitfalls and mistakes when assessing the trustworthiness of computed information, and how can they be avoided?\u003c\/b\u003e  \u003cp\u003eWhenever numerical simulation is employed in connection with engineering decision-making, there is an implied expectation of reliability: one cannot base decisions on computed information without believing that information is reliable enough to support those decisions. Using mathematical models to show the reliability of computer-generated information is an essential part of any modelling effort.\u003c\/p\u003e \u003cp\u003eGiving users of finite element analysis (FEA) software an introduction to verification and validation procedures, this book thoroughly covers the fundamentals of assuring reliability in numerical simulation. The renowned authors systematically guide readers through the basic theory and algorithmic structure of the finite element method, using helpful examples and exercises throughout.\u003c\/p\u003e \u003cul\u003e \u003cli\u003eDelivers the tools needed to have a working knowledge of the finite element method\u003c\/li\u003e \u003cli\u003eIllustrates the concepts and procedures of verification and validation \u003c\/li\u003e \u003cli\u003eExplains the process of conceptualization supported by virtual experimentation\u003c\/li\u003e \u003cli\u003eDescribes the convergence characteristics of the h-, p- and hp-methods \u003c\/li\u003e \u003cli\u003eCovers the hierarchic view of mathematical models and finite element spaces \u003c\/li\u003e \u003cli\u003eUses examples and exercises which illustrate the techniques and procedures of quality assurance \u003c\/li\u003e \u003cli\u003eIdeal for mechanical and structural engineering students, practicing engineers and applied mathematicians\u003c\/li\u003e \u003cli\u003eIncludes parameter-controlled examples of solved problems in a companion website (\u003ca href=\"http:\/\/www.wiley.com\/go\/szabo\"\u003ewww.wiley.com\/go\/szabo\u003c\/a\u003e)\u003c\/li\u003e \u003c\/ul\u003e  About the Authors.  \u003cp\u003eSeries Preface.\u003c\/p\u003e \u003cp\u003ePreface.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Numerical simulation.\u003c\/p\u003e \u003cp\u003e1.2 Why is numerical accuracy important?\u003c\/p\u003e \u003cp\u003e1.3 Chapter summary.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 An outline of the finite element method.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Mathematical models in one dimension.\u003c\/p\u003e \u003cp\u003e2.2 Approximate solution.\u003c\/p\u003e \u003cp\u003e2.3 Generalized formulation in one dimension.\u003c\/p\u003e \u003cp\u003e2.4 Finite element approximations.\u003c\/p\u003e \u003cp\u003e2.5 FEM in one dimension.\u003c\/p\u003e \u003cp\u003e2.6 Properties of the generalized formulation.\u003c\/p\u003e \u003cp\u003e2.7 Error estimation based on extrapolation.\u003c\/p\u003e \u003cp\u003e2.8 Extraction methods.\u003c\/p\u003e \u003cp\u003e2.9 Laboratory exercises.\u003c\/p\u003e \u003cp\u003e2.10 Chapter summary.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Formulation of mathematical models.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Notation.\u003c\/p\u003e \u003cp\u003e3.2 Heat conduction.\u003c\/p\u003e \u003cp\u003e3.3 The scalar elliptic boundary value problem.\u003c\/p\u003e \u003cp\u003e3.4 Linear elasticity.\u003c\/p\u003e \u003cp\u003e3.5 Incompressible elastic materials.\u003c\/p\u003e \u003cp\u003e3.6 Stokes' flow.\u003c\/p\u003e \u003cp\u003e3.7 The hierarchic view of mathematical models.\u003c\/p\u003e \u003cp\u003e3.8 Chapter summary.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Generalized formulations.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 The scalar elliptic problem.\u003c\/p\u003e \u003cp\u003e4.2 The principle of virtual work.\u003c\/p\u003e \u003cp\u003e4.3 Elastostatic problems.\u003c\/p\u003e \u003cp\u003e4.4 Elastodynamic models.\u003c\/p\u003e \u003cp\u003e4.5 Incompressible materials.\u003c\/p\u003e \u003cp\u003e4.6 Chapter summary.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Finite element spaces.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Standard elements in two dimensions.\u003c\/p\u003e \u003cp\u003e5.2 Standard polynomial spaces.\u003c\/p\u003e \u003cp\u003e5.3 Shape functions.\u003c\/p\u003e \u003cp\u003e5.4 Mapping functions in two dimensions.\u003c\/p\u003e \u003cp\u003e5.5 Elements in three dimensions.\u003c\/p\u003e \u003cp\u003e5.6 Integration and differentiation.\u003c\/p\u003e \u003cp\u003e5.7 Stiffness matrices and load vectors.\u003c\/p\u003e \u003cp\u003e5.8 Chapter summary.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Regularity and rates of convergence.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Regularity.\u003c\/p\u003e \u003cp\u003e6.2 Classification.\u003c\/p\u003e \u003cp\u003e6.3 The neighborhood of singular points.\u003c\/p\u003e \u003cp\u003e6.4 Rates of convergence.\u003c\/p\u003e \u003cp\u003e6.5 Chapter summary.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Computation and verification of data.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Computation of the solution and its first derivatives.\u003c\/p\u003e \u003cp\u003e7.2 Nodal forces.\u003c\/p\u003e \u003cp\u003e7.3 Verification of computed data.\u003c\/p\u003e \u003cp\u003e7.4 Flux and stress intensity factors.\u003c\/p\u003e \u003cp\u003e7.5 Chapter summary.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 What should be computed and why?\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Basic assumptions.\u003c\/p\u003e \u003cp\u003e8.2 Conceptualization: drivers of damage accumulation.\u003c\/p\u003e \u003cp\u003e8.3 Classical models of metal fatigue.\u003c\/p\u003e \u003cp\u003e8.4 Linear elastic fracture mechanics.\u003c\/p\u003e \u003cp\u003e8.5 On the existence of a critical distance.\u003c\/p\u003e \u003cp\u003e8.6 Driving forces for damage accumulation.\u003c\/p\u003e \u003cp\u003e8.7 Cycle counting.\u003c\/p\u003e \u003cp\u003e8.8 Validation.\u003c\/p\u003e \u003cp\u003e8.9 Chapter summary.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Beams, plates and shells.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Beams.\u003c\/p\u003e \u003cp\u003e9.2 Plates.\u003c\/p\u003e \u003cp\u003e9.3 Shells.\u003c\/p\u003e \u003cp\u003e9.4 The Oak Ridge experiments.\u003c\/p\u003e \u003cp\u003e9.5 Chapter summary.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Nonlinear models.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Heat conduction.\u003c\/p\u003e \u003cp\u003e10.2 Solid mechanics.\u003c\/p\u003e \u003cp\u003e10.3 Chapter summary.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eA Definitions.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 Norms and seminorms.\u003c\/p\u003e \u003cp\u003eA.2 Normed linear spaces.\u003c\/p\u003e \u003cp\u003eA.3 Linear functionals.\u003c\/p\u003e \u003cp\u003eA.4 Bilinear forms.\u003c\/p\u003e \u003cp\u003eA.5 Convergence.\u003c\/p\u003e \u003cp\u003eA.6 Legendre polynomials.\u003c\/p\u003e \u003cp\u003eA.7 Analytic functions.\u003c\/p\u003e \u003cp\u003eA.8 The Schwarz inequality for integrals.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eB Numerical quadrature.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eB.1 Gaussian quadrature.\u003c\/p\u003e \u003cp\u003eB.2 Gauss–Lobatto quadrature.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eC Properties of the stress tensor.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eC.1 The traction vector.\u003c\/p\u003e \u003cp\u003eC.2 Principal stresses.\u003c\/p\u003e \u003cp\u003eC.3 Transformation of vectors.\u003c\/p\u003e \u003cp\u003eC.4 Transformation of stresses.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eD Computation of stress intensity factors.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eD.1 The contour integral method.\u003c\/p\u003e \u003cp\u003eD.2 The energy release rate.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eE Saint-Venant's principle.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eE.1 Green's function for the Laplace equation.\u003c\/p\u003e \u003cp\u003eE.2 Model problem.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eF Solutions for selected exercises.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eBibliography.\u003c\/p\u003e \u003cp\u003eIndex.\u003c\/p\u003e  \u003cp\u003e“I highly recommend this as a textbook for an undergraduate engineering course on FE analysis. Moreover, I recommend this book to every engineer who practices FE computation, since this is a well-written and unique source for studying the extremely important issue of reliability of FE analysis in practice.”  (\u003ci\u003eIACM Expressions\u003c\/i\u003e, 1 September 2012)\u003c\/p\u003e  \u003cb\u003eBarna Szabó\u003c\/b\u003e is co-founder and president of Engineering Software Research and Development, Inc. (ESRD), the company that produces the professional finite element analysis software StressCheck®. Prior to his retirement from the School of Engineering and Applied Science of Washington University in 2006 he served as the Albert P. and Blanche Y. Greensfelder Professor of Mechanics. His primary research interest is assurance of quality and reliability in the numerical stimulation of structural and mechanical systems by the finite element method. He has published over 150 papers in refereed technical journals. Several of them in collaboration with Professor Ivo Babuška, with whom he also published a book on finite element analysis (John Wiley \u0026amp; Sons, Inc., 1991). He is a founding member and Fellow of the US Association for Computational Mechanics. Among his honors are election to the Hungarian Academy of Sciences as External Member and an honorary doctorate.  \u003cp\u003e\u003cb\u003eIvo Babuška\u003c\/b\u003e’s research has been concerned mainly with the reliability of computational analysis of mathematical problems and their applications, especially by the finite element method. He was the first to address a posteriori error estimation and adaptivity in finite element analysis. His research papers on these subjects published in the 1970s have been widely cited. His joint work with Barna Szabó on the p-version of the finite element method established the theoretical foundations and the algorithmic structure for this method. His recent work has been concerned with the mathematical formulation and treatment of uncertainties which are present in every mathematical model. In recognition of his numerous important contributions, Professor Babuška received may honors, which include honorary doctorates, medals and prizes and election to prestigious academies.\u003c\/p\u003e  \u003cb\u003eWhen using numerical simulation to make a decision, how can its reliability be determined? What are the common pitfalls and mistakes when assessing the trustworthiness of computed information, and how can they be avoided?\u003c\/b\u003e  \u003cp\u003eWhenever numerical simulation is employed in connection with engineering decision-making, there is an implied expectation of reliability: one cannot base decisions on computed information without believing that information is reliable enough to support those decisions. Using mathematical models to show the reliability of computer-generated information is an essential part of any modelling effort.\u003c\/p\u003e \u003cp\u003eGiving users of finite element analysis (FEA) software an introduction to verification and validation procedures, this book thoroughly covers the fundamentals of assuring reliability in numerical simulation. The renowned authors systematically guide readers through the basic theory and algorithmic structure of the finite element method, using helpful examples and exercises throughout.\u003c\/p\u003e \u003cul\u003e \u003cli\u003eDelivers the tools needed to have a working knowledge of the finite element method\u003c\/li\u003e \u003cli\u003eIllustrates the concepts and procedures of verification and validation\u003c\/li\u003e \u003cli\u003eExplains the process of conceptualization supported by virtual experimentation\u003c\/li\u003e \u003cli\u003eDescribes the convergence characteristics of the h-, p- and hp-methods\u003c\/li\u003e \u003cli\u003eCovers the hierarchic view of mathematical models and finite element spaces\u003c\/li\u003e \u003cli\u003eUses examples and exercises which illustrate the techniques and procedures of quality assurance\u003c\/li\u003e \u003cli\u003eIdeal for mechanical and structural engineering students, practicing engineers and applied mathematicians\u003c\/li\u003e \u003cli\u003eIncludes parameter-controlled examples of solved problems in a companion website (\u003ca href=\"http:\/\/www.wiley.com\/go\/szabo\"\u003ewww.wiley.com\/go\/szabo\u003c\/a\u003e)\u003c\/li\u003e \u003c\/ul\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989459779813,"sku":"NP9780470977286","price":137.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780470977286.jpg?v=1761784186","url":"https:\/\/k12savings.com\/products\/introduction-to-finite-element-analysis-isbn-9780470977286","provider":"K12savings","version":"1.0","type":"link"}